Solve 3/8x^{5}+21/40x^{4}-47/120x^3+79/120x^7+frac{1}{10}x-frac{1}{10}divfrac{1}{2}+frac{1}{9}x^2-frac{1}{4}x+frac{1}{4}x^3

$$\frac { 3 } { 8 } x ^ { 5 } + \frac { 21 } { 40 } x ^ { 4 } - \frac { 47 } { 120 } x ^ { 3 } + \frac { 79 } { 120 } x ^ { 7 } + \frac { 1 } { 10 } x - \frac { 1 } { 10 } \div \frac { 1 } { 2 } + \frac { 1 } { 9 } x ^ { 2 } - \frac { 1 } { 4 } x + \frac { 1 } { 4 } x ^ { 3 }$$

Evaluate

$$\frac{79x^{7}}{120}+\frac{3x^{5}}{8}+\frac{21x^{4}}{40}-\frac{17x^{3}}{120}+\frac{x^{2}}{9}-\frac{3x}{20}-\frac{1}{5}$$

Solution Steps

Divide \frac{1}{10} by \frac{1}{2} by multiplying \frac{1}{10} by the reciprocal of \frac{1}{2}.

$$\frac{3}{8}x^{5}+\frac{21}{40}x^{4}-\frac{47}{120}x^{3}+\frac{79}{120}x^{7}+\frac{1}{10}x-\frac{1}{10}\times 2+\frac{1}{9}x^{2}-\frac{1}{4}x+\frac{1}{4}x^{3}$$

Multiply \frac{1}{10} and 2 to get \frac{1}{5}.

$$\frac{3}{8}x^{5}+\frac{21}{40}x^{4}-\frac{47}{120}x^{3}+\frac{79}{120}x^{7}+\frac{1}{10}x-\frac{1}{5}+\frac{1}{9}x^{2}-\frac{1}{4}x+\frac{1}{4}x^{3}$$

Combine \frac{1}{10}x and -\frac{1}{4}x to get -\frac{3}{20}x.

$$\frac{3}{8}x^{5}+\frac{21}{40}x^{4}-\frac{47}{120}x^{3}+\frac{79}{120}x^{7}-\frac{3}{20}x-\frac{1}{5}+\frac{1}{9}x^{2}+\frac{1}{4}x^{3}$$

Combine -\frac{47}{120}x^{3} and \frac{1}{4}x^{3} to get -\frac{17}{120}x^{3}.

$$\frac{3}{8}x^{5}+\frac{21}{40}x^{4}-\frac{17}{120}x^{3}+\frac{79}{120}x^{7}-\frac{3}{20}x-\frac{1}{5}+\frac{1}{9}x^{2}$$

Factor

$$\frac{237x^{7}+135x^{5}+189x^{4}-51x^{3}+40x^{2}-54x-72}{360}$$

Solution Steps

Factor out \frac{1}{360}. Polynomial 237x^{7}+135x^{5}+189x^{4}-51x^{3}+40x^{2}-54x-72 is not factored since it does not have any rational roots.

$$\frac{135x^{5}+189x^{4}-141x^{3}+237x^{7}+36x-72+40x^{2}-90x+90x^{3}}{360}$$